Mathematical Methods for the Analysis of Vibrations Along the Human Arm

Abstract

Mechanical vibration is a vast field composed of thousands of studies and experiments regarding individual systems and structures’ vibrations and oscillations. The problems of vibro-safety are connected with the consideration of the human reaction to various mechanical inputs. Traditionally this problem is solved as a mechanical system with concentrated (not distributed) parameters. The goal of this study is to set up a mechanical system closely following the actual conditions of the human arm undergoing mechanical vibrations. The results will show how to generalize the analysis of the effect of vibration frequencies, and harmonic wave propagation along the human arm. In order to understand the effect on the system, a mathematical model of two viscoelastic rods connected by a hinge was derived. Using this model, it was possible to derive the propagation of both the longitudinal and bending vibrations of the arm, and find the resonance frequencies of the system from the elbow to the shoulder.